# Trigonometric Identities

ASSIGNMENT 6

7.4

Use an identity to write each expression as a single trig function value or as a single number.

14. 1 - 2 sin square 22 Â½ degree

Express as a trig function of x

22. sin 4x

Write each expression as a sum or difference

44. sin 4x sin 5x

Write each expression as a product

46. cos 5x + cos 8x

Use a half-angle identity to find the exact value

54. tan 195 degrees

76 m>1 The Mach number is the ratio of the speed of the plane and the speed of the sound. Find theta if m = 5/4

7.5 Find the exact value of each real number y

20. y = arcsin (- square root 3/2)

28. y = sec^-1 (- square root 2)

Give the degree measure of theta

36. theta = arcsin (- square root 2/2)

Give each real number

52. y = arcos .44624593

Give the exact value of each expression

66. sec (sin^-1 (-1/5))

Find each value

80. sin (cos^-1 .25)

7.6 What is the appropriate technique to begin the solution of the equation

2. sin x + 2 =3

Solve each equation over the interval (0, 2pi)

20. 2 cos square x - square root 3 cos x = 0

Solve over the interval ( 0 degree, 360 degree)

28. cos square theta = sin square theta + 1

36. 4 cos square theta + 4 cos theta + 1

Determine all solutions in radians for x or degrees for theta to the nearest tenth

44. 2 cos square x + cos x = 1

62. 2square root 3 sin 2x = square root 3

Solve over the interval (0degrees, 360 degrees)

72. -2 cos 2theta = square root 3

7.7 Solve for x

6. 4y = sin x

Solve for exact solutions

24. 4pi + 4 tan^-1 y = pi

28. arctan x = arccos 5/13

34. arccos x + 2 arcsin square root 3/2 = pi/3

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#### Solution Summary

Basixc trigonometry questions are solved using trigonometric identities.